%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC237-1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:30:37 AM UTC 2025
% Result : Unsatisfiable 1.11s 1.34s
% Output : Proof 1.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 94
% Syntax : Number of formulae : 228 ( 63 unt; 0 typ; 0 def)
% Number of atoms : 1592 ( 444 equ)
% Maximal formula atoms : 24 ( 6 avg)
% Number of connectives : 2396 (1111 ~;1155 |; 0 &)
% ( 130 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of FOOLs : 79 ( 79 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-3 aty)
% Number of variables : 475 ( 428 !; 0 ?; 475 :)
% Comments :
%------------------------------------------------------------------------------
tff(memberP_type,type,
memberP: ( $i * $i ) > $o ).
tff(sk5_type,type,
sk5: ( $i * $i * $i ) > $i ).
tff(hd_type,type,
hd: $i > $i ).
tff(sk3_type,type,
sk3: $i ).
tff(nil_type,type,
nil: $i ).
tff(skaf82_type,type,
skaf82: $i > $i ).
tff(sk1_type,type,
sk1: $i ).
tff(app_type,type,
app: ( $i * $i ) > $i ).
tff(cons_type,type,
cons: ( $i * $i ) > $i ).
tff(ssList_type,type,
ssList: $i > $o ).
tff(tl_type,type,
tl: $i > $i ).
tff(ssItem_type,type,
ssItem: $i > $o ).
tff(skaf83_type,type,
skaf83: $i > $i ).
tff(1,plain,
( ( sk1 = sk3 )
<=> ( sk1 = sk3 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_6) ).
tff(3,plain,
sk1 = sk3,
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
sk3 = sk1,
inference(symmetry,[status(thm)],[3]) ).
tff(5,plain,
( ssList(sk3)
<=> ssList(sk3) ),
inference(rewrite,[status(thm)],[]) ).
tff(6,axiom,
ssList(sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_3) ).
tff(7,plain,
ssList(sk3),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
^ [U: $i] :
refl(( ( ~ ssList(U)
| ( app(nil,U) = U ) )
<=> ( ~ ssList(U)
| ( app(nil,U) = U ) ) )),
inference(bind,[status(th)],[]) ).
tff(9,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,axiom,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause74) ).
tff(12,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
inference(skolemize,[status(sab)],[12]) ).
tff(14,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk3)
| ( app(nil,sk3) = sk3 ) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk3)
| ( app(nil,sk3) = sk3 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk3)
| ( app(nil,sk3) = sk3 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(17,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk3)
| ( app(nil,sk3) = sk3 ) ),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
app(nil,sk3) = sk3,
inference(unit_resolution,[status(thm)],[17,14,7]) ).
tff(19,plain,
( ( nil = sk1 )
<=> ( nil = sk3 ) ),
inference(monotonicity,[status(thm)],[3]) ).
tff(20,plain,
( ( nil != sk1 )
<=> ( nil != sk3 ) ),
inference(monotonicity,[status(thm)],[19]) ).
tff(21,plain,
( ( nil != sk1 )
<=> ( nil != sk1 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,axiom,
nil != sk1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
tff(23,plain,
nil != sk1,
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
nil != sk3,
inference(modus_ponens,[status(thm)],[23,20]) ).
tff(25,plain,
^ [U: $i] :
refl(( ( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) )
<=> ( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) ) )),
inference(bind,[status(th)],[]) ).
tff(26,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) ) ),
inference(quant_intro,[status(thm)],[25]) ).
tff(27,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(28,plain,
^ [U: $i] :
rewrite(( ( ~ ssList(U)
| ( cons(hd(U),tl(U)) = U )
| ( nil = U ) )
<=> ( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) ) )),
inference(bind,[status(th)],[]) ).
tff(29,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( cons(hd(U),tl(U)) = U )
| ( nil = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) ) ),
inference(quant_intro,[status(thm)],[28]) ).
tff(30,axiom,
! [U: $i] :
( ~ ssList(U)
| ( cons(hd(U),tl(U)) = U )
| ( nil = U ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause104) ).
tff(31,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) ),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) ),
inference(modus_ponens,[status(thm)],[31,27]) ).
tff(33,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) ),
inference(skolemize,[status(sab)],[32]) ).
tff(34,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) ),
inference(modus_ponens,[status(thm)],[33,26]) ).
tff(35,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ( cons(hd(sk3),tl(sk3)) = sk3 ) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ( cons(hd(sk3),tl(sk3)) = sk3 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(36,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ( cons(hd(sk3),tl(sk3)) = sk3 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(37,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(hd(U),tl(U)) = U ) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ( cons(hd(sk3),tl(sk3)) = sk3 ) ),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
cons(hd(sk3),tl(sk3)) = sk3,
inference(unit_resolution,[status(thm)],[37,34,7,24]) ).
tff(39,plain,
^ [U: $i] :
refl(( ( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
<=> ( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ) )),
inference(bind,[status(th)],[]) ).
tff(40,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ) ),
inference(quant_intro,[status(thm)],[39]) ).
tff(41,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,plain,
^ [U: $i] :
rewrite(( ( ~ ssList(U)
| ssList(tl(U))
| ( nil = U ) )
<=> ( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ) )),
inference(bind,[status(th)],[]) ).
tff(43,plain,
( ! [U: $i] :
( ~ ssList(U)
| ssList(tl(U))
| ( nil = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ) ),
inference(quant_intro,[status(thm)],[42]) ).
tff(44,axiom,
! [U: $i] :
( ~ ssList(U)
| ssList(tl(U))
| ( nil = U ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause75) ).
tff(45,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ),
inference(modus_ponens,[status(thm)],[45,41]) ).
tff(47,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ),
inference(skolemize,[status(sab)],[46]) ).
tff(48,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) ),
inference(modus_ponens,[status(thm)],[47,40]) ).
tff(49,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
| ( nil = sk3 )
| ~ ssList(sk3)
| ssList(tl(sk3)) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
| ( nil = sk3 )
| ~ ssList(sk3)
| ssList(tl(sk3)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(50,plain,
( ( ~ ssList(sk3)
| ( nil = sk3 )
| ssList(tl(sk3)) )
<=> ( ( nil = sk3 )
| ~ ssList(sk3)
| ssList(tl(sk3)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(51,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ssList(tl(sk3)) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
| ( nil = sk3 )
| ~ ssList(sk3)
| ssList(tl(sk3)) ) ),
inference(monotonicity,[status(thm)],[50]) ).
tff(52,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ssList(tl(sk3)) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
| ( nil = sk3 )
| ~ ssList(sk3)
| ssList(tl(sk3)) ) ),
inference(transitivity,[status(thm)],[51,49]) ).
tff(53,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ssList(tl(sk3)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(54,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssList(tl(U)) )
| ( nil = sk3 )
| ~ ssList(sk3)
| ssList(tl(sk3)) ),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
ssList(tl(sk3)),
inference(unit_resolution,[status(thm)],[54,48,7,24]) ).
tff(56,plain,
^ [U: $i] :
refl(( ( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
<=> ( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ) )),
inference(bind,[status(th)],[]) ).
tff(57,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ) ),
inference(quant_intro,[status(thm)],[56]) ).
tff(58,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(59,plain,
^ [U: $i] :
rewrite(( ( ~ ssList(U)
| ssItem(hd(U))
| ( nil = U ) )
<=> ( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ) )),
inference(bind,[status(th)],[]) ).
tff(60,plain,
( ! [U: $i] :
( ~ ssList(U)
| ssItem(hd(U))
| ( nil = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ) ),
inference(quant_intro,[status(thm)],[59]) ).
tff(61,axiom,
! [U: $i] :
( ~ ssList(U)
| ssItem(hd(U))
| ( nil = U ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause76) ).
tff(62,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ),
inference(modus_ponens,[status(thm)],[62,58]) ).
tff(64,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ),
inference(skolemize,[status(sab)],[63]) ).
tff(65,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) ),
inference(modus_ponens,[status(thm)],[64,57]) ).
tff(66,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
| ( nil = sk3 )
| ~ ssList(sk3)
| ssItem(hd(sk3)) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
| ( nil = sk3 )
| ~ ssList(sk3)
| ssItem(hd(sk3)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(67,plain,
( ( ~ ssList(sk3)
| ( nil = sk3 )
| ssItem(hd(sk3)) )
<=> ( ( nil = sk3 )
| ~ ssList(sk3)
| ssItem(hd(sk3)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(68,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ssItem(hd(sk3)) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
| ( nil = sk3 )
| ~ ssList(sk3)
| ssItem(hd(sk3)) ) ),
inference(monotonicity,[status(thm)],[67]) ).
tff(69,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ssItem(hd(sk3)) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
| ( nil = sk3 )
| ~ ssList(sk3)
| ssItem(hd(sk3)) ) ),
inference(transitivity,[status(thm)],[68,66]) ).
tff(70,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ssItem(hd(sk3)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(71,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ssItem(hd(U)) )
| ( nil = sk3 )
| ~ ssList(sk3)
| ssItem(hd(sk3)) ),
inference(modus_ponens,[status(thm)],[70,69]) ).
tff(72,plain,
ssItem(hd(sk3)),
inference(unit_resolution,[status(thm)],[71,65,7,24]) ).
tff(73,plain,
^ [V: $i,U: $i] :
refl(( ( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ) )),
inference(bind,[status(th)],[]) ).
tff(74,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ) ),
inference(quant_intro,[status(thm)],[73]) ).
tff(75,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(76,plain,
^ [V: $i,U: $i] :
rewrite(( ( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ) )),
inference(bind,[status(th)],[]) ).
tff(77,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ) ),
inference(quant_intro,[status(thm)],[76]) ).
tff(78,axiom,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause120) ).
tff(79,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(modus_ponens,[status(thm)],[78,77]) ).
tff(80,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(modus_ponens,[status(thm)],[79,75]) ).
tff(81,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(skolemize,[status(sab)],[80]) ).
tff(82,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(modus_ponens,[status(thm)],[81,74]) ).
tff(83,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3))
| ( app(cons(hd(sk3),nil),tl(sk3)) = cons(hd(sk3),tl(sk3)) ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3))
| ( app(cons(hd(sk3),nil),tl(sk3)) = cons(hd(sk3),tl(sk3)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(84,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3))
| ( app(cons(hd(sk3),nil),tl(sk3)) = cons(hd(sk3),tl(sk3)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(85,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3))
| ( app(cons(hd(sk3),nil),tl(sk3)) = cons(hd(sk3),tl(sk3)) ) ),
inference(modus_ponens,[status(thm)],[84,83]) ).
tff(86,plain,
( ~ ssList(tl(sk3))
| ( app(cons(hd(sk3),nil),tl(sk3)) = cons(hd(sk3),tl(sk3)) ) ),
inference(unit_resolution,[status(thm)],[85,82,72]) ).
tff(87,plain,
app(cons(hd(sk3),nil),tl(sk3)) = cons(hd(sk3),tl(sk3)),
inference(unit_resolution,[status(thm)],[86,55]) ).
tff(88,plain,
^ [U: $i] :
refl(( ssList(skaf82(U))
<=> ssList(skaf82(U)) )),
inference(bind,[status(th)],[]) ).
tff(89,plain,
( ! [U: $i] : ssList(skaf82(U))
<=> ! [U: $i] : ssList(skaf82(U)) ),
inference(quant_intro,[status(thm)],[88]) ).
tff(90,plain,
( ! [U: $i] : ssList(skaf82(U))
<=> ! [U: $i] : ssList(skaf82(U)) ),
inference(rewrite,[status(thm)],[]) ).
tff(91,axiom,
! [U: $i] : ssList(skaf82(U)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause13) ).
tff(92,plain,
! [U: $i] : ssList(skaf82(U)),
inference(modus_ponens,[status(thm)],[91,90]) ).
tff(93,plain,
! [U: $i] : ssList(skaf82(U)),
inference(skolemize,[status(sab)],[92]) ).
tff(94,plain,
! [U: $i] : ssList(skaf82(U)),
inference(modus_ponens,[status(thm)],[93,89]) ).
tff(95,plain,
( ~ ! [U: $i] : ssList(skaf82(U))
| ssList(skaf82(sk3)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(96,plain,
ssList(skaf82(sk3)),
inference(unit_resolution,[status(thm)],[95,94]) ).
tff(97,plain,
^ [U: $i] :
refl(( ssItem(skaf83(U))
<=> ssItem(skaf83(U)) )),
inference(bind,[status(th)],[]) ).
tff(98,plain,
( ! [U: $i] : ssItem(skaf83(U))
<=> ! [U: $i] : ssItem(skaf83(U)) ),
inference(quant_intro,[status(thm)],[97]) ).
tff(99,plain,
( ! [U: $i] : ssItem(skaf83(U))
<=> ! [U: $i] : ssItem(skaf83(U)) ),
inference(rewrite,[status(thm)],[]) ).
tff(100,axiom,
! [U: $i] : ssItem(skaf83(U)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause12) ).
tff(101,plain,
! [U: $i] : ssItem(skaf83(U)),
inference(modus_ponens,[status(thm)],[100,99]) ).
tff(102,plain,
! [U: $i] : ssItem(skaf83(U)),
inference(skolemize,[status(sab)],[101]) ).
tff(103,plain,
! [U: $i] : ssItem(skaf83(U)),
inference(modus_ponens,[status(thm)],[102,98]) ).
tff(104,plain,
( ~ ! [U: $i] : ssItem(skaf83(U))
| ssItem(skaf83(sk3)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(105,plain,
ssItem(skaf83(sk3)),
inference(unit_resolution,[status(thm)],[104,103]) ).
tff(106,plain,
^ [U: $i] :
refl(( ( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) )
<=> ( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) ) )),
inference(bind,[status(th)],[]) ).
tff(107,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) ) ),
inference(quant_intro,[status(thm)],[106]) ).
tff(108,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(109,plain,
^ [U: $i] :
rewrite(( ( ~ ssList(U)
| ( cons(skaf83(U),skaf82(U)) = U )
| ( nil = U ) )
<=> ( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) ) )),
inference(bind,[status(th)],[]) ).
tff(110,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( cons(skaf83(U),skaf82(U)) = U )
| ( nil = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) ) ),
inference(quant_intro,[status(thm)],[109]) ).
tff(111,axiom,
! [U: $i] :
( ~ ssList(U)
| ( cons(skaf83(U),skaf82(U)) = U )
| ( nil = U ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause109) ).
tff(112,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) ),
inference(modus_ponens,[status(thm)],[111,110]) ).
tff(113,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) ),
inference(modus_ponens,[status(thm)],[112,108]) ).
tff(114,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) ),
inference(skolemize,[status(sab)],[113]) ).
tff(115,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) ),
inference(modus_ponens,[status(thm)],[114,107]) ).
tff(116,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ( cons(skaf83(sk3),skaf82(sk3)) = sk3 ) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ( cons(skaf83(sk3),skaf82(sk3)) = sk3 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(117,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ( cons(skaf83(sk3),skaf82(sk3)) = sk3 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(118,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ( cons(skaf83(U),skaf82(U)) = U ) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ( cons(skaf83(sk3),skaf82(sk3)) = sk3 ) ),
inference(modus_ponens,[status(thm)],[117,116]) ).
tff(119,plain,
cons(skaf83(sk3),skaf82(sk3)) = sk3,
inference(unit_resolution,[status(thm)],[118,115,7,24]) ).
tff(120,plain,
sk3 = cons(skaf83(sk3),skaf82(sk3)),
inference(symmetry,[status(thm)],[119]) ).
tff(121,plain,
cons(hd(sk3),tl(sk3)) = cons(skaf83(sk3),skaf82(sk3)),
inference(transitivity,[status(thm)],[38,120]) ).
tff(122,plain,
^ [W: $i,V: $i,U: $i,X: $i] :
refl(( ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( X = V )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) )
<=> ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( X = V )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(123,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( X = V )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( X = V )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ) ),
inference(quant_intro,[status(thm)],[122]) ).
tff(124,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( X = V )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( X = V )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(125,plain,
^ [W: $i,V: $i,U: $i,X: $i] :
trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(( ( ( cons(U,V) != cons(W,X) )
| ~ ssItem(W) )
<=> ( ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ) )),
( ( ( cons(U,V) != cons(W,X) )
| ~ ssItem(W)
| ~ ssItem(U) )
<=> ( ~ ssItem(W)
| ( cons(U,V) != cons(W,X) )
| ~ ssItem(U) ) )),
rewrite(( ( ~ ssItem(W)
| ( cons(U,V) != cons(W,X) )
| ~ ssItem(U) )
<=> ( ~ ssItem(U)
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ) )),
( ( ( cons(U,V) != cons(W,X) )
| ~ ssItem(W)
| ~ ssItem(U) )
<=> ( ~ ssItem(U)
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ) )),
( ( ( cons(U,V) != cons(W,X) )
| ~ ssItem(W)
| ~ ssItem(U)
| ~ ssList(X) )
<=> ( ~ ssItem(U)
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) )
| ~ ssList(X) ) )),
rewrite(( ( ~ ssItem(U)
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) )
| ~ ssList(X) )
<=> ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ) )),
( ( ( cons(U,V) != cons(W,X) )
| ~ ssItem(W)
| ~ ssItem(U)
| ~ ssList(X) )
<=> ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ) )),
( ( ( cons(U,V) != cons(W,X) )
| ~ ssItem(W)
| ~ ssItem(U)
| ~ ssList(X)
| ~ ssList(V) )
<=> ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) )
| ~ ssList(V) ) )),
rewrite(( ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) )
| ~ ssList(V) )
<=> ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ) )),
( ( ( cons(U,V) != cons(W,X) )
| ~ ssItem(W)
| ~ ssItem(U)
| ~ ssList(X)
| ~ ssList(V) )
<=> ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ) )),
( ( ( cons(U,V) != cons(W,X) )
| ~ ssItem(W)
| ~ ssItem(U)
| ~ ssList(X)
| ~ ssList(V)
| ( X = V ) )
<=> ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) )
| ( X = V ) ) )),
rewrite(( ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) )
| ( X = V ) )
<=> ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( X = V )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ) )),
( ( ( cons(U,V) != cons(W,X) )
| ~ ssItem(W)
| ~ ssItem(U)
| ~ ssList(X)
| ~ ssList(V)
| ( X = V ) )
<=> ( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( X = V )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(126,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ( cons(U,V) != cons(W,X) )
| ~ ssItem(W)
| ~ ssItem(U)
| ~ ssList(X)
| ~ ssList(V)
| ( X = V ) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( X = V )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ) ),
inference(quant_intro,[status(thm)],[125]) ).
tff(127,axiom,
! [W: $i,V: $i,U: $i,X: $i] :
( ( cons(U,V) != cons(W,X) )
| ~ ssItem(W)
| ~ ssItem(U)
| ~ ssList(X)
| ~ ssList(V)
| ( X = V ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause171) ).
tff(128,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( X = V )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ),
inference(modus_ponens,[status(thm)],[127,126]) ).
tff(129,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( X = V )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ),
inference(modus_ponens,[status(thm)],[128,124]) ).
tff(130,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( X = V )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ),
inference(skolemize,[status(sab)],[129]) ).
tff(131,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( X = V )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) ),
inference(modus_ponens,[status(thm)],[130,123]) ).
tff(132,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( X = V )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) )
| ~ ssList(tl(sk3))
| ~ ssItem(hd(sk3))
| ~ ssList(skaf82(sk3))
| ~ ssItem(skaf83(sk3))
| ( skaf82(sk3) = tl(sk3) )
| ( cons(hd(sk3),tl(sk3)) != cons(skaf83(sk3),skaf82(sk3)) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( X = V )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) )
| ~ ssList(tl(sk3))
| ~ ssItem(hd(sk3))
| ~ ssList(skaf82(sk3))
| ~ ssItem(skaf83(sk3))
| ( skaf82(sk3) = tl(sk3) )
| ( cons(hd(sk3),tl(sk3)) != cons(skaf83(sk3),skaf82(sk3)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(133,plain,
( ( ~ ssList(skaf82(sk3))
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3))
| ( skaf82(sk3) = tl(sk3) )
| ~ ssItem(skaf83(sk3))
| ( cons(hd(sk3),tl(sk3)) != cons(skaf83(sk3),skaf82(sk3)) ) )
<=> ( ~ ssList(tl(sk3))
| ~ ssItem(hd(sk3))
| ~ ssList(skaf82(sk3))
| ~ ssItem(skaf83(sk3))
| ( skaf82(sk3) = tl(sk3) )
| ( cons(hd(sk3),tl(sk3)) != cons(skaf83(sk3),skaf82(sk3)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(134,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( X = V )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) )
| ~ ssList(skaf82(sk3))
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3))
| ( skaf82(sk3) = tl(sk3) )
| ~ ssItem(skaf83(sk3))
| ( cons(hd(sk3),tl(sk3)) != cons(skaf83(sk3),skaf82(sk3)) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( X = V )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) )
| ~ ssList(tl(sk3))
| ~ ssItem(hd(sk3))
| ~ ssList(skaf82(sk3))
| ~ ssItem(skaf83(sk3))
| ( skaf82(sk3) = tl(sk3) )
| ( cons(hd(sk3),tl(sk3)) != cons(skaf83(sk3),skaf82(sk3)) ) ) ),
inference(monotonicity,[status(thm)],[133]) ).
tff(135,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( X = V )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) )
| ~ ssList(skaf82(sk3))
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3))
| ( skaf82(sk3) = tl(sk3) )
| ~ ssItem(skaf83(sk3))
| ( cons(hd(sk3),tl(sk3)) != cons(skaf83(sk3),skaf82(sk3)) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( X = V )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) )
| ~ ssList(tl(sk3))
| ~ ssItem(hd(sk3))
| ~ ssList(skaf82(sk3))
| ~ ssItem(skaf83(sk3))
| ( skaf82(sk3) = tl(sk3) )
| ( cons(hd(sk3),tl(sk3)) != cons(skaf83(sk3),skaf82(sk3)) ) ) ),
inference(transitivity,[status(thm)],[134,132]) ).
tff(136,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( X = V )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) )
| ~ ssList(skaf82(sk3))
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3))
| ( skaf82(sk3) = tl(sk3) )
| ~ ssItem(skaf83(sk3))
| ( cons(hd(sk3),tl(sk3)) != cons(skaf83(sk3),skaf82(sk3)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(137,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssList(V)
| ( X = V )
| ~ ssItem(W)
| ( cons(U,V) != cons(W,X) ) )
| ~ ssList(tl(sk3))
| ~ ssItem(hd(sk3))
| ~ ssList(skaf82(sk3))
| ~ ssItem(skaf83(sk3))
| ( skaf82(sk3) = tl(sk3) )
| ( cons(hd(sk3),tl(sk3)) != cons(skaf83(sk3),skaf82(sk3)) ) ),
inference(modus_ponens,[status(thm)],[136,135]) ).
tff(138,plain,
( ~ ssList(tl(sk3))
| ~ ssList(skaf82(sk3))
| ~ ssItem(skaf83(sk3))
| ( skaf82(sk3) = tl(sk3) ) ),
inference(unit_resolution,[status(thm)],[137,131,72,121]) ).
tff(139,plain,
skaf82(sk3) = tl(sk3),
inference(unit_resolution,[status(thm)],[138,55,105,96]) ).
tff(140,plain,
app(cons(hd(sk3),nil),skaf82(sk3)) = app(cons(hd(sk3),nil),tl(sk3)),
inference(monotonicity,[status(thm)],[139]) ).
tff(141,plain,
app(cons(hd(sk3),nil),skaf82(sk3)) = sk3,
inference(transitivity,[status(thm)],[140,87,38]) ).
tff(142,plain,
app(nil,app(cons(hd(sk3),nil),skaf82(sk3))) = app(nil,sk3),
inference(monotonicity,[status(thm)],[141]) ).
tff(143,plain,
^ [V: $i,U: $i] :
refl(( ( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ) )),
inference(bind,[status(th)],[]) ).
tff(144,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ) ),
inference(quant_intro,[status(thm)],[143]) ).
tff(145,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(146,plain,
^ [V: $i,U: $i] :
rewrite(( ( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ) )),
inference(bind,[status(th)],[]) ).
tff(147,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ) ),
inference(quant_intro,[status(thm)],[146]) ).
tff(148,axiom,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause86) ).
tff(149,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[148,147]) ).
tff(150,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[149,145]) ).
tff(151,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(skolemize,[status(sab)],[150]) ).
tff(152,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[151,144]) ).
tff(153,plain,
( ssList(nil)
<=> ssList(nil) ),
inference(rewrite,[status(thm)],[]) ).
tff(154,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause8) ).
tff(155,plain,
ssList(nil),
inference(modus_ponens,[status(thm)],[154,153]) ).
tff(156,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssList(nil)
| ~ ssItem(hd(sk3))
| ssList(cons(hd(sk3),nil)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssList(nil)
| ~ ssItem(hd(sk3))
| ssList(cons(hd(sk3),nil)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(157,plain,
( ( ~ ssItem(hd(sk3))
| ~ ssList(nil)
| ssList(cons(hd(sk3),nil)) )
<=> ( ~ ssList(nil)
| ~ ssItem(hd(sk3))
| ssList(cons(hd(sk3),nil)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(158,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(hd(sk3))
| ~ ssList(nil)
| ssList(cons(hd(sk3),nil)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssList(nil)
| ~ ssItem(hd(sk3))
| ssList(cons(hd(sk3),nil)) ) ),
inference(monotonicity,[status(thm)],[157]) ).
tff(159,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(hd(sk3))
| ~ ssList(nil)
| ssList(cons(hd(sk3),nil)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssList(nil)
| ~ ssItem(hd(sk3))
| ssList(cons(hd(sk3),nil)) ) ),
inference(transitivity,[status(thm)],[158,156]) ).
tff(160,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(hd(sk3))
| ~ ssList(nil)
| ssList(cons(hd(sk3),nil)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(161,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssList(nil)
| ~ ssItem(hd(sk3))
| ssList(cons(hd(sk3),nil)) ),
inference(modus_ponens,[status(thm)],[160,159]) ).
tff(162,plain,
ssList(cons(hd(sk3),nil)),
inference(unit_resolution,[status(thm)],[161,155,152,72]) ).
tff(163,plain,
^ [W: $i,V: $i,U: $i] :
refl(( ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(164,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ) ),
inference(quant_intro,[status(thm)],[163]) ).
tff(165,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(166,plain,
^ [W: $i,V: $i,U: $i] :
trans(monotonicity(rewrite(( ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W) ) )),
( ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ) )),
rewrite(( ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ) )),
( ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(167,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ) ),
inference(quant_intro,[status(thm)],[166]) ).
tff(168,axiom,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause149) ).
tff(169,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ),
inference(modus_ponens,[status(thm)],[168,167]) ).
tff(170,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ),
inference(modus_ponens,[status(thm)],[169,165]) ).
tff(171,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ),
inference(skolemize,[status(sab)],[170]) ).
tff(172,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ),
inference(modus_ponens,[status(thm)],[171,164]) ).
tff(173,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(nil)
| ~ ssList(skaf82(sk3))
| ~ ssList(cons(hd(sk3),nil))
| ( app(app(nil,cons(hd(sk3),nil)),skaf82(sk3)) = app(nil,app(cons(hd(sk3),nil),skaf82(sk3))) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(nil)
| ~ ssList(skaf82(sk3))
| ~ ssList(cons(hd(sk3),nil))
| ( app(app(nil,cons(hd(sk3),nil)),skaf82(sk3)) = app(nil,app(cons(hd(sk3),nil),skaf82(sk3))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(174,plain,
( ( ~ ssList(skaf82(sk3))
| ~ ssList(cons(hd(sk3),nil))
| ~ ssList(nil)
| ( app(app(nil,cons(hd(sk3),nil)),skaf82(sk3)) = app(nil,app(cons(hd(sk3),nil),skaf82(sk3))) ) )
<=> ( ~ ssList(nil)
| ~ ssList(skaf82(sk3))
| ~ ssList(cons(hd(sk3),nil))
| ( app(app(nil,cons(hd(sk3),nil)),skaf82(sk3)) = app(nil,app(cons(hd(sk3),nil),skaf82(sk3))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(175,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(skaf82(sk3))
| ~ ssList(cons(hd(sk3),nil))
| ~ ssList(nil)
| ( app(app(nil,cons(hd(sk3),nil)),skaf82(sk3)) = app(nil,app(cons(hd(sk3),nil),skaf82(sk3))) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(nil)
| ~ ssList(skaf82(sk3))
| ~ ssList(cons(hd(sk3),nil))
| ( app(app(nil,cons(hd(sk3),nil)),skaf82(sk3)) = app(nil,app(cons(hd(sk3),nil),skaf82(sk3))) ) ) ),
inference(monotonicity,[status(thm)],[174]) ).
tff(176,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(skaf82(sk3))
| ~ ssList(cons(hd(sk3),nil))
| ~ ssList(nil)
| ( app(app(nil,cons(hd(sk3),nil)),skaf82(sk3)) = app(nil,app(cons(hd(sk3),nil),skaf82(sk3))) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(nil)
| ~ ssList(skaf82(sk3))
| ~ ssList(cons(hd(sk3),nil))
| ( app(app(nil,cons(hd(sk3),nil)),skaf82(sk3)) = app(nil,app(cons(hd(sk3),nil),skaf82(sk3))) ) ) ),
inference(transitivity,[status(thm)],[175,173]) ).
tff(177,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(skaf82(sk3))
| ~ ssList(cons(hd(sk3),nil))
| ~ ssList(nil)
| ( app(app(nil,cons(hd(sk3),nil)),skaf82(sk3)) = app(nil,app(cons(hd(sk3),nil),skaf82(sk3))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(178,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(nil)
| ~ ssList(skaf82(sk3))
| ~ ssList(cons(hd(sk3),nil))
| ( app(app(nil,cons(hd(sk3),nil)),skaf82(sk3)) = app(nil,app(cons(hd(sk3),nil),skaf82(sk3))) ) ),
inference(modus_ponens,[status(thm)],[177,176]) ).
tff(179,plain,
app(app(nil,cons(hd(sk3),nil)),skaf82(sk3)) = app(nil,app(cons(hd(sk3),nil),skaf82(sk3))),
inference(unit_resolution,[status(thm)],[178,155,172,96,162]) ).
tff(180,plain,
app(app(nil,cons(hd(sk3),nil)),skaf82(sk3)) = sk1,
inference(transitivity,[status(thm)],[179,142,18,4]) ).
tff(181,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| memberP(B,sk5(C,B,A)) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| memberP(B,sk5(C,B,A)) ) )),
inference(bind,[status(th)],[]) ).
tff(182,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| memberP(B,sk5(C,B,A)) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| memberP(B,sk5(C,B,A)) ) ),
inference(quant_intro,[status(thm)],[181]) ).
tff(183,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| memberP(B,sk5(C,B,A)) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| memberP(B,sk5(C,B,A)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(184,plain,
^ [B: $i,A: $i,C: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 ) ) )),
rewrite(( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| memberP(B,sk5(C,B,A)) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| memberP(B,sk5(C,B,A)) ) )),
rewrite(( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| memberP(B,sk5(C,B,A)) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| memberP(B,sk5(C,B,A)) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| memberP(B,sk5(C,B,A)) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| memberP(B,sk5(C,B,A)) ) )),
inference(bind,[status(th)],[]) ).
tff(185,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| memberP(B,sk5(C,B,A)) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| memberP(B,sk5(C,B,A)) ) ),
inference(quant_intro,[status(thm)],[184]) ).
tff(186,axiom,
! [B: $i,A: $i,C: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| memberP(B,sk5(C,B,A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_9) ).
tff(187,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| memberP(B,sk5(C,B,A)) ),
inference(modus_ponens,[status(thm)],[186,185]) ).
tff(188,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| memberP(B,sk5(C,B,A)) ),
inference(modus_ponens,[status(thm)],[187,183]) ).
tff(189,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| memberP(B,sk5(C,B,A)) ),
inference(skolemize,[status(sab)],[188]) ).
tff(190,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| memberP(B,sk5(C,B,A)) ),
inference(modus_ponens,[status(thm)],[189,182]) ).
tff(191,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| memberP(B,sk5(C,B,A)) )
| ~ ssList(nil)
| ~ ssItem(hd(sk3))
| ~ ssList(skaf82(sk3))
| ( app(app(nil,cons(hd(sk3),nil)),skaf82(sk3)) != sk1 )
| memberP(nil,sk5(skaf82(sk3),nil,hd(sk3))) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| memberP(B,sk5(C,B,A)) )
| ~ ssList(nil)
| ~ ssItem(hd(sk3))
| ~ ssList(skaf82(sk3))
| ( app(app(nil,cons(hd(sk3),nil)),skaf82(sk3)) != sk1 )
| memberP(nil,sk5(skaf82(sk3),nil,hd(sk3))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(192,plain,
( ( ~ ssList(skaf82(sk3))
| ~ ssItem(hd(sk3))
| ~ ssList(nil)
| ( app(app(nil,cons(hd(sk3),nil)),skaf82(sk3)) != sk1 )
| memberP(nil,sk5(skaf82(sk3),nil,hd(sk3))) )
<=> ( ~ ssList(nil)
| ~ ssItem(hd(sk3))
| ~ ssList(skaf82(sk3))
| ( app(app(nil,cons(hd(sk3),nil)),skaf82(sk3)) != sk1 )
| memberP(nil,sk5(skaf82(sk3),nil,hd(sk3))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(193,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| memberP(B,sk5(C,B,A)) )
| ~ ssList(skaf82(sk3))
| ~ ssItem(hd(sk3))
| ~ ssList(nil)
| ( app(app(nil,cons(hd(sk3),nil)),skaf82(sk3)) != sk1 )
| memberP(nil,sk5(skaf82(sk3),nil,hd(sk3))) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| memberP(B,sk5(C,B,A)) )
| ~ ssList(nil)
| ~ ssItem(hd(sk3))
| ~ ssList(skaf82(sk3))
| ( app(app(nil,cons(hd(sk3),nil)),skaf82(sk3)) != sk1 )
| memberP(nil,sk5(skaf82(sk3),nil,hd(sk3))) ) ),
inference(monotonicity,[status(thm)],[192]) ).
tff(194,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| memberP(B,sk5(C,B,A)) )
| ~ ssList(skaf82(sk3))
| ~ ssItem(hd(sk3))
| ~ ssList(nil)
| ( app(app(nil,cons(hd(sk3),nil)),skaf82(sk3)) != sk1 )
| memberP(nil,sk5(skaf82(sk3),nil,hd(sk3))) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| memberP(B,sk5(C,B,A)) )
| ~ ssList(nil)
| ~ ssItem(hd(sk3))
| ~ ssList(skaf82(sk3))
| ( app(app(nil,cons(hd(sk3),nil)),skaf82(sk3)) != sk1 )
| memberP(nil,sk5(skaf82(sk3),nil,hd(sk3))) ) ),
inference(transitivity,[status(thm)],[193,191]) ).
tff(195,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| memberP(B,sk5(C,B,A)) )
| ~ ssList(skaf82(sk3))
| ~ ssItem(hd(sk3))
| ~ ssList(nil)
| ( app(app(nil,cons(hd(sk3),nil)),skaf82(sk3)) != sk1 )
| memberP(nil,sk5(skaf82(sk3),nil,hd(sk3))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(196,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| memberP(B,sk5(C,B,A)) )
| ~ ssList(nil)
| ~ ssItem(hd(sk3))
| ~ ssList(skaf82(sk3))
| ( app(app(nil,cons(hd(sk3),nil)),skaf82(sk3)) != sk1 )
| memberP(nil,sk5(skaf82(sk3),nil,hd(sk3))) ),
inference(modus_ponens,[status(thm)],[195,194]) ).
tff(197,plain,
memberP(nil,sk5(skaf82(sk3),nil,hd(sk3))),
inference(unit_resolution,[status(thm)],[196,155,190,72,96,180]) ).
tff(198,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) ) )),
inference(bind,[status(th)],[]) ).
tff(199,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) ) ),
inference(quant_intro,[status(thm)],[198]) ).
tff(200,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(201,plain,
^ [B: $i,A: $i,C: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 ) ) )),
rewrite(( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ssItem(sk5(C,B,A)) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ssItem(sk5(C,B,A)) ) )),
rewrite(( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ssItem(sk5(C,B,A)) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ssItem(sk5(C,B,A)) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) ) )),
inference(bind,[status(th)],[]) ).
tff(202,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ssItem(sk5(C,B,A)) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) ) ),
inference(quant_intro,[status(thm)],[201]) ).
tff(203,axiom,
! [B: $i,A: $i,C: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ssItem(sk5(C,B,A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
tff(204,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) ),
inference(modus_ponens,[status(thm)],[203,202]) ).
tff(205,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) ),
inference(modus_ponens,[status(thm)],[204,200]) ).
tff(206,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) ),
inference(skolemize,[status(sab)],[205]) ).
tff(207,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) ),
inference(modus_ponens,[status(thm)],[206,199]) ).
tff(208,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) )
| ~ ssList(nil)
| ~ ssItem(hd(sk3))
| ~ ssList(skaf82(sk3))
| ( app(app(nil,cons(hd(sk3),nil)),skaf82(sk3)) != sk1 )
| ssItem(sk5(skaf82(sk3),nil,hd(sk3))) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) )
| ~ ssList(nil)
| ~ ssItem(hd(sk3))
| ~ ssList(skaf82(sk3))
| ( app(app(nil,cons(hd(sk3),nil)),skaf82(sk3)) != sk1 )
| ssItem(sk5(skaf82(sk3),nil,hd(sk3))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(209,plain,
( ( ~ ssList(skaf82(sk3))
| ~ ssItem(hd(sk3))
| ~ ssList(nil)
| ssItem(sk5(skaf82(sk3),nil,hd(sk3)))
| ( app(app(nil,cons(hd(sk3),nil)),skaf82(sk3)) != sk1 ) )
<=> ( ~ ssList(nil)
| ~ ssItem(hd(sk3))
| ~ ssList(skaf82(sk3))
| ( app(app(nil,cons(hd(sk3),nil)),skaf82(sk3)) != sk1 )
| ssItem(sk5(skaf82(sk3),nil,hd(sk3))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(210,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) )
| ~ ssList(skaf82(sk3))
| ~ ssItem(hd(sk3))
| ~ ssList(nil)
| ssItem(sk5(skaf82(sk3),nil,hd(sk3)))
| ( app(app(nil,cons(hd(sk3),nil)),skaf82(sk3)) != sk1 ) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) )
| ~ ssList(nil)
| ~ ssItem(hd(sk3))
| ~ ssList(skaf82(sk3))
| ( app(app(nil,cons(hd(sk3),nil)),skaf82(sk3)) != sk1 )
| ssItem(sk5(skaf82(sk3),nil,hd(sk3))) ) ),
inference(monotonicity,[status(thm)],[209]) ).
tff(211,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) )
| ~ ssList(skaf82(sk3))
| ~ ssItem(hd(sk3))
| ~ ssList(nil)
| ssItem(sk5(skaf82(sk3),nil,hd(sk3)))
| ( app(app(nil,cons(hd(sk3),nil)),skaf82(sk3)) != sk1 ) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) )
| ~ ssList(nil)
| ~ ssItem(hd(sk3))
| ~ ssList(skaf82(sk3))
| ( app(app(nil,cons(hd(sk3),nil)),skaf82(sk3)) != sk1 )
| ssItem(sk5(skaf82(sk3),nil,hd(sk3))) ) ),
inference(transitivity,[status(thm)],[210,208]) ).
tff(212,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) )
| ~ ssList(skaf82(sk3))
| ~ ssItem(hd(sk3))
| ~ ssList(nil)
| ssItem(sk5(skaf82(sk3),nil,hd(sk3)))
| ( app(app(nil,cons(hd(sk3),nil)),skaf82(sk3)) != sk1 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(213,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) )
| ~ ssList(nil)
| ~ ssItem(hd(sk3))
| ~ ssList(skaf82(sk3))
| ( app(app(nil,cons(hd(sk3),nil)),skaf82(sk3)) != sk1 )
| ssItem(sk5(skaf82(sk3),nil,hd(sk3))) ),
inference(modus_ponens,[status(thm)],[212,211]) ).
tff(214,plain,
ssItem(sk5(skaf82(sk3),nil,hd(sk3))),
inference(unit_resolution,[status(thm)],[213,155,207,72,96,180]) ).
tff(215,plain,
^ [U: $i] :
refl(( ( ~ ssItem(U)
| ~ memberP(nil,U) )
<=> ( ~ ssItem(U)
| ~ memberP(nil,U) ) )),
inference(bind,[status(th)],[]) ).
tff(216,plain,
( ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) )
<=> ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ) ),
inference(quant_intro,[status(thm)],[215]) ).
tff(217,plain,
( ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) )
<=> ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(218,plain,
^ [U: $i] :
rewrite(( ( ~ memberP(nil,U)
| ~ ssItem(U) )
<=> ( ~ ssItem(U)
| ~ memberP(nil,U) ) )),
inference(bind,[status(th)],[]) ).
tff(219,plain,
( ! [U: $i] :
( ~ memberP(nil,U)
| ~ ssItem(U) )
<=> ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ) ),
inference(quant_intro,[status(thm)],[218]) ).
tff(220,axiom,
! [U: $i] :
( ~ memberP(nil,U)
| ~ ssItem(U) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause71) ).
tff(221,plain,
! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ),
inference(modus_ponens,[status(thm)],[220,219]) ).
tff(222,plain,
! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ),
inference(modus_ponens,[status(thm)],[221,217]) ).
tff(223,plain,
! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ),
inference(skolemize,[status(sab)],[222]) ).
tff(224,plain,
! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ),
inference(modus_ponens,[status(thm)],[223,216]) ).
tff(225,plain,
( ( ~ ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) )
| ~ ssItem(sk5(skaf82(sk3),nil,hd(sk3)))
| ~ memberP(nil,sk5(skaf82(sk3),nil,hd(sk3))) )
<=> ( ~ ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) )
| ~ ssItem(sk5(skaf82(sk3),nil,hd(sk3)))
| ~ memberP(nil,sk5(skaf82(sk3),nil,hd(sk3))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(226,plain,
( ~ ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) )
| ~ ssItem(sk5(skaf82(sk3),nil,hd(sk3)))
| ~ memberP(nil,sk5(skaf82(sk3),nil,hd(sk3))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(227,plain,
( ~ ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) )
| ~ ssItem(sk5(skaf82(sk3),nil,hd(sk3)))
| ~ memberP(nil,sk5(skaf82(sk3),nil,hd(sk3))) ),
inference(modus_ponens,[status(thm)],[226,225]) ).
tff(228,plain,
$false,
inference(unit_resolution,[status(thm)],[227,224,214,197]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWC237-1 : TPTP v9.0.0. Released v2.4.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n009.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 08:41:33 EDT 2025
% 0.11/0.33 % CPUTime :
% 1.11/1.34 % SZS status Unsatisfiable
% 1.11/1.34 % SZS output start Proof
% See solution above
% 1.21/1.37 % E exiting
%------------------------------------------------------------------------------